Properties

Label 120.2.d.a.109.3
Level 120
Weight 2
Character 120.109
Analytic conductor 0.958
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.839056.1
Defining polynomial: \(x^{6} + 6 x^{4} + 8 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.3
Root \(2.02852i\) of defining polynomial
Character \(\chi\) \(=\) 120.109
Dual form 120.2.d.a.109.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.321037 - 1.37729i) q^{2} +1.00000 q^{3} +(-1.79387 + 0.884323i) q^{4} +(2.11491 + 0.726062i) q^{5} +(-0.321037 - 1.37729i) q^{6} -4.05705i q^{7} +(1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.321037 - 1.37729i) q^{2} +1.00000 q^{3} +(-1.79387 + 0.884323i) q^{4} +(2.11491 + 0.726062i) q^{5} +(-0.321037 - 1.37729i) q^{6} -4.05705i q^{7} +(1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +(0.321037 - 3.14594i) q^{10} +0.985939i q^{11} +(-1.79387 + 0.884323i) q^{12} -4.94567 q^{13} +(-5.58774 + 1.30246i) q^{14} +(2.11491 + 0.726062i) q^{15} +(2.43594 - 3.17272i) q^{16} +4.52323i q^{17} +(-0.321037 - 1.37729i) q^{18} +2.60492i q^{19} +(-4.43594 + 0.567801i) q^{20} -4.05705i q^{21} +(1.35793 - 0.316523i) q^{22} -3.53729i q^{23} +(1.79387 + 2.18678i) q^{24} +(3.94567 + 3.07111i) q^{25} +(1.58774 + 6.81163i) q^{26} +1.00000 q^{27} +(3.58774 + 7.27782i) q^{28} +7.59434i q^{29} +(0.321037 - 3.14594i) q^{30} -3.28415 q^{31} +(-5.15180 - 2.33645i) q^{32} +0.985939i q^{33} +(6.22982 - 1.45212i) q^{34} +(2.94567 - 8.58028i) q^{35} +(-1.79387 + 0.884323i) q^{36} +0.945668 q^{37} +(3.58774 - 0.836276i) q^{38} -4.94567 q^{39} +(2.20613 + 5.92731i) q^{40} +0.568295 q^{41} +(-5.58774 + 1.30246i) q^{42} -8.45963 q^{43} +(-0.871889 - 1.76865i) q^{44} +(2.11491 + 0.726062i) q^{45} +(-4.87189 + 1.13560i) q^{46} +2.60492i q^{47} +(2.43594 - 3.17272i) q^{48} -9.45963 q^{49} +(2.96311 - 6.42028i) q^{50} +4.52323i q^{51} +(8.87189 - 4.37357i) q^{52} -0.229815 q^{53} +(-0.321037 - 1.37729i) q^{54} +(-0.715853 + 2.08517i) q^{55} +(8.87189 - 7.27782i) q^{56} +2.60492i q^{57} +(10.4596 - 2.43806i) q^{58} -9.10003i q^{59} +(-4.43594 + 0.567801i) q^{60} -11.0183i q^{61} +(1.05433 + 4.52323i) q^{62} -4.05705i q^{63} +(-1.56406 + 7.84562i) q^{64} +(-10.4596 - 3.59086i) q^{65} +(1.35793 - 0.316523i) q^{66} +8.45963 q^{67} +(-4.00000 - 8.11409i) q^{68} -3.53729i q^{69} +(-12.7632 - 1.30246i) q^{70} +1.43171 q^{71} +(1.79387 + 2.18678i) q^{72} -11.9507i q^{73} +(-0.303594 - 1.30246i) q^{74} +(3.94567 + 3.07111i) q^{75} +(-2.30359 - 4.67289i) q^{76} +4.00000 q^{77} +(1.58774 + 6.81163i) q^{78} +3.28415 q^{79} +(7.45539 - 4.94137i) q^{80} +1.00000 q^{81} +(-0.182443 - 0.782708i) q^{82} -9.89134 q^{83} +(3.58774 + 7.27782i) q^{84} +(-3.28415 + 9.56622i) q^{85} +(2.71585 + 11.6514i) q^{86} +7.59434i q^{87} +(-2.15604 + 1.76865i) q^{88} +12.3510 q^{89} +(0.321037 - 3.14594i) q^{90} +20.0648i q^{91} +(3.12811 + 6.34545i) q^{92} -3.28415 q^{93} +(3.58774 - 0.836276i) q^{94} +(-1.89134 + 5.50917i) q^{95} +(-5.15180 - 2.33645i) q^{96} -3.23797i q^{97} +(3.03689 + 13.0287i) q^{98} +0.985939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 6q^{3} + q^{4} - q^{6} - q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - q^{2} + 6q^{3} + q^{4} - q^{6} - q^{8} + 6q^{9} + q^{10} + q^{12} - 8q^{13} - 10q^{14} + q^{16} - q^{18} - 13q^{20} + 10q^{22} - q^{24} + 2q^{25} - 14q^{26} + 6q^{27} - 2q^{28} + q^{30} - 16q^{31} - 21q^{32} + 12q^{34} - 4q^{35} + q^{36} - 16q^{37} - 2q^{38} - 8q^{39} + 25q^{40} - 4q^{41} - 10q^{42} + 22q^{44} - 2q^{46} + q^{48} - 6q^{49} + 15q^{50} + 26q^{52} + 24q^{53} - q^{54} - 8q^{55} + 26q^{56} + 12q^{58} - 13q^{60} + 28q^{62} - 23q^{64} - 12q^{65} + 10q^{66} - 24q^{68} - 6q^{70} + 16q^{71} - q^{72} + 18q^{74} + 2q^{75} + 6q^{76} + 24q^{77} - 14q^{78} + 16q^{79} + 15q^{80} + 6q^{81} - 50q^{82} - 16q^{83} - 2q^{84} - 16q^{85} + 20q^{86} + 18q^{88} - 20q^{89} + q^{90} + 46q^{92} - 16q^{93} - 2q^{94} + 32q^{95} - 21q^{96} + 21q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.321037 1.37729i −0.227007 0.973893i
\(3\) 1.00000 0.577350
\(4\) −1.79387 + 0.884323i −0.896935 + 0.442162i
\(5\) 2.11491 + 0.726062i 0.945815 + 0.324705i
\(6\) −0.321037 1.37729i −0.131063 0.562277i
\(7\) 4.05705i 1.53342i −0.641994 0.766710i \(-0.721893\pi\)
0.641994 0.766710i \(-0.278107\pi\)
\(8\) 1.79387 + 2.18678i 0.634229 + 0.773145i
\(9\) 1.00000 0.333333
\(10\) 0.321037 3.14594i 0.101521 0.994833i
\(11\) 0.985939i 0.297272i 0.988892 + 0.148636i \(0.0474882\pi\)
−0.988892 + 0.148636i \(0.952512\pi\)
\(12\) −1.79387 + 0.884323i −0.517846 + 0.255282i
\(13\) −4.94567 −1.37168 −0.685841 0.727752i \(-0.740565\pi\)
−0.685841 + 0.727752i \(0.740565\pi\)
\(14\) −5.58774 + 1.30246i −1.49339 + 0.348097i
\(15\) 2.11491 + 0.726062i 0.546067 + 0.187468i
\(16\) 2.43594 3.17272i 0.608986 0.793181i
\(17\) 4.52323i 1.09704i 0.836136 + 0.548522i \(0.184809\pi\)
−0.836136 + 0.548522i \(0.815191\pi\)
\(18\) −0.321037 1.37729i −0.0756691 0.324631i
\(19\) 2.60492i 0.597610i 0.954314 + 0.298805i \(0.0965881\pi\)
−0.954314 + 0.298805i \(0.903412\pi\)
\(20\) −4.43594 + 0.567801i −0.991907 + 0.126964i
\(21\) 4.05705i 0.885320i
\(22\) 1.35793 0.316523i 0.289511 0.0674829i
\(23\) 3.53729i 0.737577i −0.929513 0.368788i \(-0.879773\pi\)
0.929513 0.368788i \(-0.120227\pi\)
\(24\) 1.79387 + 2.18678i 0.366172 + 0.446376i
\(25\) 3.94567 + 3.07111i 0.789134 + 0.614222i
\(26\) 1.58774 + 6.81163i 0.311382 + 1.33587i
\(27\) 1.00000 0.192450
\(28\) 3.58774 + 7.27782i 0.678019 + 1.37538i
\(29\) 7.59434i 1.41023i 0.709091 + 0.705117i \(0.249105\pi\)
−0.709091 + 0.705117i \(0.750895\pi\)
\(30\) 0.321037 3.14594i 0.0586130 0.574367i
\(31\) −3.28415 −0.589850 −0.294925 0.955520i \(-0.595295\pi\)
−0.294925 + 0.955520i \(0.595295\pi\)
\(32\) −5.15180 2.33645i −0.910718 0.413029i
\(33\) 0.985939i 0.171630i
\(34\) 6.22982 1.45212i 1.06840 0.249037i
\(35\) 2.94567 8.58028i 0.497909 1.45033i
\(36\) −1.79387 + 0.884323i −0.298978 + 0.147387i
\(37\) 0.945668 0.155467 0.0777334 0.996974i \(-0.475232\pi\)
0.0777334 + 0.996974i \(0.475232\pi\)
\(38\) 3.58774 0.836276i 0.582009 0.135662i
\(39\) −4.94567 −0.791941
\(40\) 2.20613 + 5.92731i 0.348820 + 0.937190i
\(41\) 0.568295 0.0887527 0.0443763 0.999015i \(-0.485870\pi\)
0.0443763 + 0.999015i \(0.485870\pi\)
\(42\) −5.58774 + 1.30246i −0.862207 + 0.200974i
\(43\) −8.45963 −1.29008 −0.645041 0.764148i \(-0.723160\pi\)
−0.645041 + 0.764148i \(0.723160\pi\)
\(44\) −0.871889 1.76865i −0.131442 0.266634i
\(45\) 2.11491 + 0.726062i 0.315272 + 0.108235i
\(46\) −4.87189 + 1.13560i −0.718321 + 0.167435i
\(47\) 2.60492i 0.379967i 0.981787 + 0.189984i \(0.0608435\pi\)
−0.981787 + 0.189984i \(0.939157\pi\)
\(48\) 2.43594 3.17272i 0.351598 0.457943i
\(49\) −9.45963 −1.35138
\(50\) 2.96311 6.42028i 0.419047 0.907964i
\(51\) 4.52323i 0.633379i
\(52\) 8.87189 4.37357i 1.23031 0.606505i
\(53\) −0.229815 −0.0315675 −0.0157838 0.999875i \(-0.505024\pi\)
−0.0157838 + 0.999875i \(0.505024\pi\)
\(54\) −0.321037 1.37729i −0.0436876 0.187426i
\(55\) −0.715853 + 2.08517i −0.0965256 + 0.281164i
\(56\) 8.87189 7.27782i 1.18556 0.972539i
\(57\) 2.60492i 0.345030i
\(58\) 10.4596 2.43806i 1.37342 0.320133i
\(59\) 9.10003i 1.18472i −0.805672 0.592362i \(-0.798196\pi\)
0.805672 0.592362i \(-0.201804\pi\)
\(60\) −4.43594 + 0.567801i −0.572678 + 0.0733028i
\(61\) 11.0183i 1.41075i −0.708832 0.705377i \(-0.750778\pi\)
0.708832 0.705377i \(-0.249222\pi\)
\(62\) 1.05433 + 4.52323i 0.133900 + 0.574451i
\(63\) 4.05705i 0.511140i
\(64\) −1.56406 + 7.84562i −0.195507 + 0.980702i
\(65\) −10.4596 3.59086i −1.29736 0.445392i
\(66\) 1.35793 0.316523i 0.167149 0.0389612i
\(67\) 8.45963 1.03351 0.516754 0.856134i \(-0.327140\pi\)
0.516754 + 0.856134i \(0.327140\pi\)
\(68\) −4.00000 8.11409i −0.485071 0.983978i
\(69\) 3.53729i 0.425840i
\(70\) −12.7632 1.30246i −1.52550 0.155674i
\(71\) 1.43171 0.169912 0.0849561 0.996385i \(-0.472925\pi\)
0.0849561 + 0.996385i \(0.472925\pi\)
\(72\) 1.79387 + 2.18678i 0.211410 + 0.257715i
\(73\) 11.9507i 1.39873i −0.714767 0.699363i \(-0.753467\pi\)
0.714767 0.699363i \(-0.246533\pi\)
\(74\) −0.303594 1.30246i −0.0352921 0.151408i
\(75\) 3.94567 + 3.07111i 0.455606 + 0.354621i
\(76\) −2.30359 4.67289i −0.264240 0.536018i
\(77\) 4.00000 0.455842
\(78\) 1.58774 + 6.81163i 0.179776 + 0.771266i
\(79\) 3.28415 0.369495 0.184748 0.982786i \(-0.440853\pi\)
0.184748 + 0.982786i \(0.440853\pi\)
\(80\) 7.45539 4.94137i 0.833538 0.552462i
\(81\) 1.00000 0.111111
\(82\) −0.182443 0.782708i −0.0201475 0.0864356i
\(83\) −9.89134 −1.08572 −0.542858 0.839825i \(-0.682658\pi\)
−0.542858 + 0.839825i \(0.682658\pi\)
\(84\) 3.58774 + 7.27782i 0.391455 + 0.794075i
\(85\) −3.28415 + 9.56622i −0.356216 + 1.03760i
\(86\) 2.71585 + 11.6514i 0.292858 + 1.25640i
\(87\) 7.59434i 0.814199i
\(88\) −2.15604 + 1.76865i −0.229834 + 0.188538i
\(89\) 12.3510 1.30920 0.654600 0.755976i \(-0.272837\pi\)
0.654600 + 0.755976i \(0.272837\pi\)
\(90\) 0.321037 3.14594i 0.0338403 0.331611i
\(91\) 20.0648i 2.10336i
\(92\) 3.12811 + 6.34545i 0.326128 + 0.661559i
\(93\) −3.28415 −0.340550
\(94\) 3.58774 0.836276i 0.370047 0.0862553i
\(95\) −1.89134 + 5.50917i −0.194047 + 0.565229i
\(96\) −5.15180 2.33645i −0.525803 0.238463i
\(97\) 3.23797i 0.328766i −0.986397 0.164383i \(-0.947437\pi\)
0.986397 0.164383i \(-0.0525633\pi\)
\(98\) 3.03689 + 13.0287i 0.306772 + 1.31610i
\(99\) 0.985939i 0.0990906i
\(100\) −9.79387 2.01992i −0.979387 0.201992i
\(101\) 4.35637i 0.433475i −0.976230 0.216738i \(-0.930458\pi\)
0.976230 0.216738i \(-0.0695416\pi\)
\(102\) 6.22982 1.45212i 0.616844 0.143782i
\(103\) 15.0754i 1.48542i 0.669612 + 0.742711i \(0.266460\pi\)
−0.669612 + 0.742711i \(0.733540\pi\)
\(104\) −8.87189 10.8151i −0.869960 1.06051i
\(105\) 2.94567 8.58028i 0.287468 0.837350i
\(106\) 0.0737791 + 0.316523i 0.00716606 + 0.0307434i
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −1.79387 + 0.884323i −0.172615 + 0.0850941i
\(109\) 4.17034i 0.399446i −0.979852 0.199723i \(-0.935996\pi\)
0.979852 0.199723i \(-0.0640042\pi\)
\(110\) 3.10170 + 0.316523i 0.295736 + 0.0301793i
\(111\) 0.945668 0.0897588
\(112\) −12.8719 9.88274i −1.21628 0.933831i
\(113\) 1.28526i 0.120907i 0.998171 + 0.0604537i \(0.0192548\pi\)
−0.998171 + 0.0604537i \(0.980745\pi\)
\(114\) 3.58774 0.836276i 0.336023 0.0783244i
\(115\) 2.56829 7.48105i 0.239495 0.697611i
\(116\) −6.71585 13.6233i −0.623551 1.26489i
\(117\) −4.94567 −0.457227
\(118\) −12.5334 + 2.92145i −1.15379 + 0.268941i
\(119\) 18.3510 1.68223
\(120\) 2.20613 + 5.92731i 0.201391 + 0.541087i
\(121\) 10.0279 0.911630
\(122\) −15.1755 + 3.53729i −1.37392 + 0.320252i
\(123\) 0.568295 0.0512414
\(124\) 5.89134 2.90425i 0.529058 0.260809i
\(125\) 6.11491 + 9.35991i 0.546934 + 0.837176i
\(126\) −5.58774 + 1.30246i −0.497796 + 0.116032i
\(127\) 1.15280i 0.102294i −0.998691 0.0511472i \(-0.983712\pi\)
0.998691 0.0511472i \(-0.0162878\pi\)
\(128\) 11.3078 0.364570i 0.999481 0.0322237i
\(129\) −8.45963 −0.744829
\(130\) −1.58774 + 15.5588i −0.139254 + 1.36459i
\(131\) 3.89019i 0.339887i 0.985454 + 0.169944i \(0.0543586\pi\)
−0.985454 + 0.169944i \(0.945641\pi\)
\(132\) −0.871889 1.76865i −0.0758882 0.153941i
\(133\) 10.5683 0.916387
\(134\) −2.71585 11.6514i −0.234614 1.00653i
\(135\) 2.11491 + 0.726062i 0.182022 + 0.0624895i
\(136\) −9.89134 + 8.11409i −0.848175 + 0.695778i
\(137\) 17.5135i 1.49628i −0.663544 0.748138i \(-0.730948\pi\)
0.663544 0.748138i \(-0.269052\pi\)
\(138\) −4.87189 + 1.13560i −0.414723 + 0.0966688i
\(139\) 16.8612i 1.43015i −0.699047 0.715076i \(-0.746392\pi\)
0.699047 0.715076i \(-0.253608\pi\)
\(140\) 2.30359 + 17.9968i 0.194689 + 1.52101i
\(141\) 2.60492i 0.219374i
\(142\) −0.459630 1.97188i −0.0385713 0.165476i
\(143\) 4.87613i 0.407762i
\(144\) 2.43594 3.17272i 0.202995 0.264394i
\(145\) −5.51396 + 16.0613i −0.457910 + 1.33382i
\(146\) −16.4596 + 3.83662i −1.36221 + 0.317521i
\(147\) −9.45963 −0.780217
\(148\) −1.69641 + 0.836276i −0.139444 + 0.0687415i
\(149\) 10.4986i 0.860078i 0.902810 + 0.430039i \(0.141500\pi\)
−0.902810 + 0.430039i \(0.858500\pi\)
\(150\) 2.96311 6.42028i 0.241937 0.524214i
\(151\) 4.71585 0.383771 0.191885 0.981417i \(-0.438540\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(152\) −5.69641 + 4.67289i −0.462040 + 0.379022i
\(153\) 4.52323i 0.365682i
\(154\) −1.28415 5.50917i −0.103480 0.443942i
\(155\) −6.94567 2.38449i −0.557889 0.191527i
\(156\) 8.87189 4.37357i 0.710320 0.350166i
\(157\) 8.94567 0.713942 0.356971 0.934115i \(-0.383809\pi\)
0.356971 + 0.934115i \(0.383809\pi\)
\(158\) −1.05433 4.52323i −0.0838782 0.359849i
\(159\) −0.229815 −0.0182255
\(160\) −9.19917 8.68189i −0.727258 0.686364i
\(161\) −14.3510 −1.13101
\(162\) −0.321037 1.37729i −0.0252230 0.108210i
\(163\) 15.7827 1.23619 0.618097 0.786102i \(-0.287904\pi\)
0.618097 + 0.786102i \(0.287904\pi\)
\(164\) −1.01945 + 0.502556i −0.0796054 + 0.0392430i
\(165\) −0.715853 + 2.08517i −0.0557291 + 0.162330i
\(166\) 3.17548 + 13.6233i 0.246465 + 1.05737i
\(167\) 5.50917i 0.426312i 0.977018 + 0.213156i \(0.0683743\pi\)
−0.977018 + 0.213156i \(0.931626\pi\)
\(168\) 8.87189 7.27782i 0.684481 0.561496i
\(169\) 11.4596 0.881510
\(170\) 14.2298 + 1.45212i 1.09138 + 0.111373i
\(171\) 2.60492i 0.199203i
\(172\) 15.1755 7.48105i 1.15712 0.570425i
\(173\) −10.3385 −0.786020 −0.393010 0.919534i \(-0.628566\pi\)
−0.393010 + 0.919534i \(0.628566\pi\)
\(174\) 10.4596 2.43806i 0.792943 0.184829i
\(175\) 12.4596 16.0078i 0.941860 1.21007i
\(176\) 3.12811 + 2.40169i 0.235790 + 0.181034i
\(177\) 9.10003i 0.684000i
\(178\) −3.96511 17.0109i −0.297198 1.27502i
\(179\) 16.1746i 1.20895i 0.796625 + 0.604474i \(0.206617\pi\)
−0.796625 + 0.604474i \(0.793383\pi\)
\(180\) −4.43594 + 0.567801i −0.330636 + 0.0423214i
\(181\) 8.11409i 0.603116i −0.953448 0.301558i \(-0.902493\pi\)
0.953448 0.301558i \(-0.0975067\pi\)
\(182\) 27.6351 6.44154i 2.04845 0.477479i
\(183\) 11.0183i 0.814499i
\(184\) 7.73530 6.34545i 0.570254 0.467793i
\(185\) 2.00000 + 0.686614i 0.147043 + 0.0504808i
\(186\) 1.05433 + 4.52323i 0.0773074 + 0.331659i
\(187\) −4.45963 −0.326120
\(188\) −2.30359 4.67289i −0.168007 0.340806i
\(189\) 4.05705i 0.295107i
\(190\) 8.19493 + 0.836276i 0.594523 + 0.0606698i
\(191\) −24.9193 −1.80309 −0.901547 0.432681i \(-0.857568\pi\)
−0.901547 + 0.432681i \(0.857568\pi\)
\(192\) −1.56406 + 7.84562i −0.112876 + 0.566209i
\(193\) 1.03951i 0.0748254i −0.999300 0.0374127i \(-0.988088\pi\)
0.999300 0.0374127i \(-0.0119116\pi\)
\(194\) −4.45963 + 1.03951i −0.320183 + 0.0746323i
\(195\) −10.4596 3.59086i −0.749030 0.257147i
\(196\) 16.9694 8.36537i 1.21210 0.597527i
\(197\) −9.66152 −0.688355 −0.344177 0.938905i \(-0.611842\pi\)
−0.344177 + 0.938905i \(0.611842\pi\)
\(198\) 1.35793 0.316523i 0.0965036 0.0224943i
\(199\) −23.0668 −1.63516 −0.817582 0.575813i \(-0.804686\pi\)
−0.817582 + 0.575813i \(0.804686\pi\)
\(200\) 0.362165 + 14.1375i 0.0256090 + 0.999672i
\(201\) 8.45963 0.596696
\(202\) −6.00000 + 1.39856i −0.422159 + 0.0984020i
\(203\) 30.8106 2.16248
\(204\) −4.00000 8.11409i −0.280056 0.568100i
\(205\) 1.20189 + 0.412617i 0.0839437 + 0.0288184i
\(206\) 20.7632 4.83975i 1.44664 0.337202i
\(207\) 3.53729i 0.245859i
\(208\) −12.0474 + 15.6912i −0.835335 + 1.08799i
\(209\) −2.56829 −0.177653
\(210\) −12.7632 1.30246i −0.880746 0.0898784i
\(211\) 6.44154i 0.443454i −0.975109 0.221727i \(-0.928831\pi\)
0.975109 0.221727i \(-0.0711694\pi\)
\(212\) 0.412259 0.203231i 0.0283140 0.0139580i
\(213\) 1.43171 0.0980988
\(214\) 1.28415 + 5.50917i 0.0877825 + 0.376599i
\(215\) −17.8913 6.14222i −1.22018 0.418896i
\(216\) 1.79387 + 2.18678i 0.122057 + 0.148792i
\(217\) 13.3239i 0.904488i
\(218\) −5.74378 + 1.33883i −0.389018 + 0.0906772i
\(219\) 11.9507i 0.807554i
\(220\) −0.559817 4.37357i −0.0377428 0.294866i
\(221\) 22.3704i 1.50480i
\(222\) −0.303594 1.30246i −0.0203759 0.0874155i
\(223\) 17.9796i 1.20401i 0.798494 + 0.602003i \(0.205630\pi\)
−0.798494 + 0.602003i \(0.794370\pi\)
\(224\) −9.47908 + 20.9011i −0.633347 + 1.39651i
\(225\) 3.94567 + 3.07111i 0.263045 + 0.204741i
\(226\) 1.77018 0.412617i 0.117751 0.0274469i
\(227\) −7.02792 −0.466460 −0.233230 0.972422i \(-0.574929\pi\)
−0.233230 + 0.972422i \(0.574929\pi\)
\(228\) −2.30359 4.67289i −0.152559 0.309470i
\(229\) 4.17034i 0.275584i 0.990461 + 0.137792i \(0.0440005\pi\)
−0.990461 + 0.137792i \(0.955999\pi\)
\(230\) −11.1281 1.13560i −0.733766 0.0748793i
\(231\) 4.00000 0.263181
\(232\) −16.6072 + 13.6233i −1.09032 + 0.894411i
\(233\) 23.9894i 1.57160i 0.618483 + 0.785799i \(0.287748\pi\)
−0.618483 + 0.785799i \(0.712252\pi\)
\(234\) 1.58774 + 6.81163i 0.103794 + 0.445290i
\(235\) −1.89134 + 5.50917i −0.123377 + 0.359379i
\(236\) 8.04737 + 16.3243i 0.523839 + 1.06262i
\(237\) 3.28415 0.213328
\(238\) −5.89134 25.2747i −0.381879 1.63831i
\(239\) 8.91926 0.576939 0.288469 0.957489i \(-0.406854\pi\)
0.288469 + 0.957489i \(0.406854\pi\)
\(240\) 7.45539 4.94137i 0.481243 0.318964i
\(241\) −16.3510 −1.05326 −0.526629 0.850095i \(-0.676544\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(242\) −3.21933 13.8114i −0.206947 0.887830i
\(243\) 1.00000 0.0641500
\(244\) 9.74378 + 19.7655i 0.623781 + 1.26536i
\(245\) −20.0062 6.86828i −1.27815 0.438798i
\(246\) −0.182443 0.782708i −0.0116322 0.0499036i
\(247\) 12.8831i 0.819731i
\(248\) −5.89134 7.18172i −0.374100 0.456040i
\(249\) −9.89134 −0.626838
\(250\) 10.9282 11.4269i 0.691162 0.722700i
\(251\) 4.22391i 0.266611i 0.991075 + 0.133305i \(0.0425591\pi\)
−0.991075 + 0.133305i \(0.957441\pi\)
\(252\) 3.58774 + 7.27782i 0.226006 + 0.458459i
\(253\) 3.48755 0.219261
\(254\) −1.58774 + 0.370091i −0.0996238 + 0.0232216i
\(255\) −3.28415 + 9.56622i −0.205661 + 0.599060i
\(256\) −4.13235 15.4572i −0.258272 0.966072i
\(257\) 24.6952i 1.54044i 0.637777 + 0.770221i \(0.279854\pi\)
−0.637777 + 0.770221i \(0.720146\pi\)
\(258\) 2.71585 + 11.6514i 0.169082 + 0.725384i
\(259\) 3.83662i 0.238396i
\(260\) 21.9387 2.80815i 1.36058 0.174154i
\(261\) 7.59434i 0.470078i
\(262\) 5.35793 1.24889i 0.331014 0.0771569i
\(263\) 14.6628i 0.904145i −0.891981 0.452073i \(-0.850685\pi\)
0.891981 0.452073i \(-0.149315\pi\)
\(264\) −2.15604 + 1.76865i −0.132695 + 0.108853i
\(265\) −0.486038 0.166860i −0.0298571 0.0102501i
\(266\) −3.39281 14.5556i −0.208027 0.892463i
\(267\) 12.3510 0.755867
\(268\) −15.1755 + 7.48105i −0.926990 + 0.456978i
\(269\) 11.5381i 0.703490i −0.936096 0.351745i \(-0.885588\pi\)
0.936096 0.351745i \(-0.114412\pi\)
\(270\) 0.321037 3.14594i 0.0195377 0.191456i
\(271\) 5.63511 0.342309 0.171154 0.985244i \(-0.445250\pi\)
0.171154 + 0.985244i \(0.445250\pi\)
\(272\) 14.3510 + 11.0183i 0.870155 + 0.668085i
\(273\) 20.0648i 1.21438i
\(274\) −24.1212 + 5.62246i −1.45721 + 0.339665i
\(275\) −3.02792 + 3.89019i −0.182591 + 0.234587i
\(276\) 3.12811 + 6.34545i 0.188290 + 0.381951i
\(277\) −17.4053 −1.04578 −0.522892 0.852399i \(-0.675147\pi\)
−0.522892 + 0.852399i \(0.675147\pi\)
\(278\) −23.2229 + 5.41308i −1.39281 + 0.324655i
\(279\) −3.28415 −0.196617
\(280\) 24.0474 8.95037i 1.43711 0.534887i
\(281\) 21.7827 1.29945 0.649723 0.760171i \(-0.274885\pi\)
0.649723 + 0.760171i \(0.274885\pi\)
\(282\) 3.58774 0.836276i 0.213647 0.0497995i
\(283\) −21.5962 −1.28376 −0.641881 0.766804i \(-0.721846\pi\)
−0.641881 + 0.766804i \(0.721846\pi\)
\(284\) −2.56829 + 1.26609i −0.152400 + 0.0751287i
\(285\) −1.89134 + 5.50917i −0.112033 + 0.326335i
\(286\) −6.71585 + 1.56542i −0.397117 + 0.0925650i
\(287\) 2.30560i 0.136095i
\(288\) −5.15180 2.33645i −0.303573 0.137676i
\(289\) −3.45963 −0.203508
\(290\) 23.8913 + 2.43806i 1.40295 + 0.143168i
\(291\) 3.23797i 0.189813i
\(292\) 10.5683 + 21.4380i 0.618463 + 1.25457i
\(293\) 32.0125 1.87019 0.935095 0.354398i \(-0.115314\pi\)
0.935095 + 0.354398i \(0.115314\pi\)
\(294\) 3.03689 + 13.0287i 0.177115 + 0.759848i
\(295\) 6.60719 19.2457i 0.384685 1.12053i
\(296\) 1.69641 + 2.06797i 0.0986016 + 0.120198i
\(297\) 0.985939i 0.0572100i
\(298\) 14.4596 3.37043i 0.837624 0.195244i
\(299\) 17.4943i 1.01172i
\(300\) −9.79387 2.01992i −0.565449 0.116620i
\(301\) 34.3211i 1.97824i
\(302\) −1.51396 6.49511i −0.0871187 0.373752i
\(303\) 4.35637i 0.250267i
\(304\) 8.26470 + 6.34545i 0.474013 + 0.363936i
\(305\) 8.00000 23.3028i 0.458079 1.33431i
\(306\) 6.22982 1.45212i 0.356135 0.0830124i
\(307\) 1.13659 0.0648686 0.0324343 0.999474i \(-0.489674\pi\)
0.0324343 + 0.999474i \(0.489674\pi\)
\(308\) −7.17548 + 3.53729i −0.408861 + 0.201556i
\(309\) 15.0754i 0.857609i
\(310\) −1.05433 + 10.3317i −0.0598820 + 0.586803i
\(311\) 5.13659 0.291269 0.145635 0.989338i \(-0.453478\pi\)
0.145635 + 0.989338i \(0.453478\pi\)
\(312\) −8.87189 10.8151i −0.502272 0.612285i
\(313\) 23.0762i 1.30434i −0.758071 0.652172i \(-0.773858\pi\)
0.758071 0.652172i \(-0.226142\pi\)
\(314\) −2.87189 12.3208i −0.162070 0.695303i
\(315\) 2.94567 8.58028i 0.165970 0.483444i
\(316\) −5.89134 + 2.90425i −0.331414 + 0.163377i
\(317\) −1.66152 −0.0933203 −0.0466601 0.998911i \(-0.514858\pi\)
−0.0466601 + 0.998911i \(0.514858\pi\)
\(318\) 0.0737791 + 0.316523i 0.00413733 + 0.0177497i
\(319\) −7.48755 −0.419223
\(320\) −9.00424 + 15.4572i −0.503352 + 0.864081i
\(321\) −4.00000 −0.223258
\(322\) 4.60719 + 19.7655i 0.256749 + 1.10149i
\(323\) −11.7827 −0.655605
\(324\) −1.79387 + 0.884323i −0.0996595 + 0.0491291i
\(325\) −19.5140 15.1887i −1.08244 0.842516i
\(326\) −5.06682 21.7374i −0.280625 1.20392i
\(327\) 4.17034i 0.230620i
\(328\) 1.01945 + 1.24274i 0.0562895 + 0.0686187i
\(329\) 10.5683 0.582649
\(330\) 3.10170 + 0.316523i 0.170743 + 0.0174240i
\(331\) 25.9077i 1.42402i −0.702171 0.712008i \(-0.747786\pi\)
0.702171 0.712008i \(-0.252214\pi\)
\(332\) 17.7438 8.74714i 0.973816 0.480062i
\(333\) 0.945668 0.0518223
\(334\) 7.58774 1.76865i 0.415183 0.0967760i
\(335\) 17.8913 + 6.14222i 0.977508 + 0.335585i
\(336\) −12.8719 9.88274i −0.702219 0.539148i
\(337\) 8.00696i 0.436167i 0.975930 + 0.218083i \(0.0699805\pi\)
−0.975930 + 0.218083i \(0.930020\pi\)
\(338\) −3.67896 15.7833i −0.200109 0.858496i
\(339\) 1.28526i 0.0698060i
\(340\) −2.56829 20.0648i −0.139285 1.08817i
\(341\) 3.23797i 0.175346i
\(342\) 3.58774 0.836276i 0.194003 0.0452206i
\(343\) 9.97884i 0.538806i
\(344\) −15.1755 18.4994i −0.818207 0.997420i
\(345\) 2.56829 7.48105i 0.138272 0.402766i
\(346\) 3.31903 + 14.2391i 0.178432 + 0.765499i
\(347\) 23.0279 1.23620 0.618102 0.786098i \(-0.287902\pi\)
0.618102 + 0.786098i \(0.287902\pi\)
\(348\) −6.71585 13.6233i −0.360007 0.730284i
\(349\) 21.4380i 1.14755i 0.819012 + 0.573776i \(0.194522\pi\)
−0.819012 + 0.573776i \(0.805478\pi\)
\(350\) −26.0474 12.0215i −1.39229 0.642575i
\(351\) −4.94567 −0.263980
\(352\) 2.30359 5.07936i 0.122782 0.270731i
\(353\) 4.52323i 0.240747i 0.992729 + 0.120374i \(0.0384093\pi\)
−0.992729 + 0.120374i \(0.961591\pi\)
\(354\) −12.5334 + 2.92145i −0.666143 + 0.155273i
\(355\) 3.02792 + 1.03951i 0.160706 + 0.0551713i
\(356\) −22.1560 + 10.9222i −1.17427 + 0.578878i
\(357\) 18.3510 0.971236
\(358\) 22.2772 5.19265i 1.17739 0.274440i
\(359\) −10.3510 −0.546303 −0.273152 0.961971i \(-0.588066\pi\)
−0.273152 + 0.961971i \(0.588066\pi\)
\(360\) 2.20613 + 5.92731i 0.116273 + 0.312397i
\(361\) 12.2144 0.642862
\(362\) −11.1755 + 2.60492i −0.587370 + 0.136912i
\(363\) 10.0279 0.526330
\(364\) −17.7438 35.9937i −0.930027 1.88658i
\(365\) 8.67696 25.2747i 0.454173 1.32294i
\(366\) −15.1755 + 3.53729i −0.793235 + 0.184897i
\(367\) 0.485359i 0.0253355i −0.999920 0.0126678i \(-0.995968\pi\)
0.999920 0.0126678i \(-0.00403238\pi\)
\(368\) −11.2229 8.61665i −0.585032 0.449174i
\(369\) 0.568295 0.0295842
\(370\) 0.303594 2.97501i 0.0157831 0.154664i
\(371\) 0.932371i 0.0484063i
\(372\) 5.89134 2.90425i 0.305452 0.150578i
\(373\) 30.0823 1.55760 0.778800 0.627272i \(-0.215829\pi\)
0.778800 + 0.627272i \(0.215829\pi\)
\(374\) 1.43171 + 6.14222i 0.0740317 + 0.317606i
\(375\) 6.11491 + 9.35991i 0.315772 + 0.483344i
\(376\) −5.69641 + 4.67289i −0.293770 + 0.240986i
\(377\) 37.5591i 1.93439i
\(378\) −5.58774 + 1.30246i −0.287402 + 0.0669914i
\(379\) 33.6881i 1.73044i 0.501392 + 0.865220i \(0.332821\pi\)
−0.501392 + 0.865220i \(0.667179\pi\)
\(380\) −1.47908 11.5553i −0.0758751 0.592774i
\(381\) 1.15280i 0.0590597i
\(382\) 8.00000 + 34.3211i 0.409316 + 1.75602i
\(383\) 5.17545i 0.264453i 0.991220 + 0.132227i \(0.0422127\pi\)
−0.991220 + 0.132227i \(0.957787\pi\)
\(384\) 11.3078 0.364570i 0.577050 0.0186044i
\(385\) 8.45963 + 2.90425i 0.431143 + 0.148014i
\(386\) −1.43171 + 0.333720i −0.0728719 + 0.0169859i
\(387\) −8.45963 −0.430027
\(388\) 2.86341 + 5.80850i 0.145368 + 0.294882i
\(389\) 16.6408i 0.843722i −0.906660 0.421861i \(-0.861377\pi\)
0.906660 0.421861i \(-0.138623\pi\)
\(390\) −1.58774 + 15.5588i −0.0803984 + 0.787849i
\(391\) 16.0000 0.809155
\(392\) −16.9694 20.6862i −0.857082 1.04481i
\(393\) 3.89019i 0.196234i
\(394\) 3.10170 + 13.3067i 0.156262 + 0.670384i
\(395\) 6.94567 + 2.38449i 0.349474 + 0.119977i
\(396\) −0.871889 1.76865i −0.0438141 0.0888778i
\(397\) −20.4332 −1.02551 −0.512757 0.858534i \(-0.671376\pi\)
−0.512757 + 0.858534i \(0.671376\pi\)
\(398\) 7.40530 + 31.7698i 0.371194 + 1.59247i
\(399\) 10.5683 0.529076
\(400\) 19.3552 5.03746i 0.967760 0.251873i
\(401\) −4.56829 −0.228130 −0.114065 0.993473i \(-0.536387\pi\)
−0.114065 + 0.993473i \(0.536387\pi\)
\(402\) −2.71585 11.6514i −0.135454 0.581118i
\(403\) 16.2423 0.809087
\(404\) 3.85244 + 7.81477i 0.191666 + 0.388799i
\(405\) 2.11491 + 0.726062i 0.105091 + 0.0360783i
\(406\) −9.89134 42.4352i −0.490899 2.10602i
\(407\) 0.932371i 0.0462159i
\(408\) −9.89134 + 8.11409i −0.489694 + 0.401708i
\(409\) −19.8913 −0.983563 −0.491782 0.870719i \(-0.663654\pi\)
−0.491782 + 0.870719i \(0.663654\pi\)
\(410\) 0.182443 1.78782i 0.00901024 0.0882941i
\(411\) 17.5135i 0.863875i
\(412\) −13.3315 27.0433i −0.656797 1.33233i
\(413\) −36.9193 −1.81668
\(414\) −4.87189 + 1.13560i −0.239440 + 0.0558118i
\(415\) −20.9193 7.18172i −1.02689 0.352537i
\(416\) 25.4791 + 11.5553i 1.24921 + 0.566545i
\(417\) 16.8612i 0.825698i
\(418\) 0.824517 + 3.53729i 0.0403284 + 0.173015i
\(419\) 0.387288i 0.0189203i −0.999955 0.00946013i \(-0.996989\pi\)
0.999955 0.00946013i \(-0.00301130\pi\)
\(420\) 2.30359 + 17.9968i 0.112404 + 0.878156i
\(421\) 12.0578i 0.587664i 0.955857 + 0.293832i \(0.0949306\pi\)
−0.955857 + 0.293832i \(0.905069\pi\)
\(422\) −8.87189 + 2.06797i −0.431877 + 0.100667i
\(423\) 2.60492i 0.126656i
\(424\) −0.412259 0.502556i −0.0200210 0.0244063i
\(425\) −13.8913 + 17.8472i −0.673829 + 0.865715i
\(426\) −0.459630 1.97188i −0.0222692 0.0955378i
\(427\) −44.7019 −2.16328
\(428\) 7.17548 3.53729i 0.346840 0.170982i
\(429\) 4.87613i 0.235422i
\(430\) −2.71585 + 26.6135i −0.130970 + 1.28342i
\(431\) 40.4068 1.94633 0.973164 0.230113i \(-0.0739096\pi\)
0.973164 + 0.230113i \(0.0739096\pi\)
\(432\) 2.43594 3.17272i 0.117199 0.152648i
\(433\) 36.1859i 1.73898i −0.493949 0.869491i \(-0.664447\pi\)
0.493949 0.869491i \(-0.335553\pi\)
\(434\) 18.3510 4.27748i 0.880875 0.205325i
\(435\) −5.51396 + 16.0613i −0.264374 + 0.770082i
\(436\) 3.68793 + 7.48105i 0.176620 + 0.358277i
\(437\) 9.21438 0.440783
\(438\) −16.4596 + 3.83662i −0.786472 + 0.183321i
\(439\) 25.4178 1.21312 0.606562 0.795036i \(-0.292548\pi\)
0.606562 + 0.795036i \(0.292548\pi\)
\(440\) −5.84396 + 2.17511i −0.278600 + 0.103694i
\(441\) −9.45963 −0.450459
\(442\) −30.8106 + 7.18172i −1.46551 + 0.341600i
\(443\) 7.02792 0.333907 0.166953 0.985965i \(-0.446607\pi\)
0.166953 + 0.985965i \(0.446607\pi\)
\(444\) −1.69641 + 0.836276i −0.0805079 + 0.0396879i
\(445\) 26.1212 + 8.96757i 1.23826 + 0.425103i
\(446\) 24.7632 5.77213i 1.17257 0.273318i
\(447\) 10.4986i 0.496566i
\(448\) 31.8300 + 6.34545i 1.50383 + 0.299794i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 2.96311 6.42028i 0.139682 0.302655i
\(451\) 0.560304i 0.0263837i
\(452\) −1.13659 2.30560i −0.0534607 0.108446i
\(453\) 4.71585 0.221570
\(454\) 2.25622 + 9.67951i 0.105890 + 0.454282i
\(455\) −14.5683 + 42.4352i −0.682972 + 1.98939i
\(456\) −5.69641 + 4.67289i −0.266759 + 0.218828i
\(457\) 25.2747i 1.18230i 0.806562 + 0.591149i \(0.201326\pi\)
−0.806562 + 0.591149i \(0.798674\pi\)
\(458\) 5.74378 1.33883i 0.268389 0.0625595i
\(459\) 4.52323i 0.211126i
\(460\) 2.00848 + 15.6912i 0.0936458 + 0.731608i
\(461\) 41.0902i 1.91376i 0.290479 + 0.956881i \(0.406185\pi\)
−0.290479 + 0.956881i \(0.593815\pi\)
\(462\) −1.28415 5.50917i −0.0597439 0.256310i
\(463\) 13.2106i 0.613951i 0.951717 + 0.306975i \(0.0993169\pi\)
−0.951717 + 0.306975i \(0.900683\pi\)
\(464\) 24.0947 + 18.4994i 1.11857 + 0.858813i
\(465\) −6.94567 2.38449i −0.322098 0.110578i
\(466\) 33.0404 7.70148i 1.53057 0.356764i
\(467\) 1.89134 0.0875206 0.0437603 0.999042i \(-0.486066\pi\)
0.0437603 + 0.999042i \(0.486066\pi\)
\(468\) 8.87189 4.37357i 0.410103 0.202168i
\(469\) 34.3211i 1.58480i
\(470\) 8.19493 + 0.836276i 0.378004 + 0.0385745i
\(471\) 8.94567 0.412195
\(472\) 19.8998 16.3243i 0.915963 0.751386i
\(473\) 8.34068i 0.383505i
\(474\) −1.05433 4.52323i −0.0484271 0.207759i
\(475\) −8.00000 + 10.2782i −0.367065 + 0.471594i
\(476\) −32.9193 + 16.2282i −1.50885 + 0.743818i
\(477\) −0.229815 −0.0105225
\(478\) −2.86341 12.2844i −0.130969 0.561877i
\(479\) −31.4876 −1.43870 −0.719352 0.694646i \(-0.755561\pi\)
−0.719352 + 0.694646i \(0.755561\pi\)
\(480\) −9.19917 8.68189i −0.419883 0.396272i
\(481\) −4.67696 −0.213251
\(482\) 5.24926 + 22.5201i 0.239097 + 1.02576i
\(483\) −14.3510 −0.652992
\(484\) −17.9888 + 8.86793i −0.817673 + 0.403088i
\(485\) 2.35097 6.84800i 0.106752 0.310952i
\(486\) −0.321037 1.37729i −0.0145625 0.0624753i
\(487\) 12.9964i 0.588922i 0.955664 + 0.294461i \(0.0951401\pi\)
−0.955664 + 0.294461i \(0.904860\pi\)
\(488\) 24.0947 19.7655i 1.09072 0.894741i
\(489\) 15.7827 0.713717
\(490\) −3.03689 + 29.7594i −0.137193 + 1.34439i
\(491\) 14.9085i 0.672812i −0.941717 0.336406i \(-0.890788\pi\)
0.941717 0.336406i \(-0.109212\pi\)
\(492\) −1.01945 + 0.502556i −0.0459602 + 0.0226570i
\(493\) −34.3510 −1.54709
\(494\) −17.7438 + 4.13594i −0.798330 + 0.186085i
\(495\) −0.715853 + 2.08517i −0.0321752 + 0.0937214i
\(496\) −8.00000 + 10.4197i −0.359211 + 0.467858i
\(497\) 5.80850i 0.260547i
\(498\) 3.17548 + 13.6233i 0.142297 + 0.610473i
\(499\) 35.6599i 1.59636i −0.602420 0.798179i \(-0.705797\pi\)
0.602420 0.798179i \(-0.294203\pi\)
\(500\) −19.2465 11.3829i −0.860731 0.509059i
\(501\) 5.50917i 0.246132i
\(502\) 5.81756 1.35603i 0.259650 0.0605226i
\(503\) 25.3090i 1.12847i 0.825613 + 0.564237i \(0.190830\pi\)
−0.825613 + 0.564237i \(0.809170\pi\)
\(504\) 8.87189 7.27782i 0.395185 0.324180i
\(505\) 3.16300 9.21332i 0.140751 0.409988i
\(506\) −1.11963 4.80338i −0.0497738 0.213536i
\(507\) 11.4596 0.508940
\(508\) 1.01945 + 2.06797i 0.0452306 + 0.0917514i
\(509\) 13.7366i 0.608862i −0.952534 0.304431i \(-0.901534\pi\)
0.952534 0.304431i \(-0.0984663\pi\)
\(510\) 14.2298 + 1.45212i 0.630107 + 0.0643011i
\(511\) −48.4846 −2.14483
\(512\) −19.9624 + 10.6538i −0.882221 + 0.470835i
\(513\) 2.60492i 0.115010i
\(514\) 34.0125 7.92806i 1.50023 0.349692i
\(515\) −10.9457 + 31.8831i −0.482324 + 1.40494i
\(516\) 15.1755 7.48105i 0.668063 0.329335i
\(517\) −2.56829 −0.112953
\(518\) −5.28415 + 1.23170i −0.232172 + 0.0541176i
\(519\) −10.3385 −0.453809
\(520\) −10.9108 29.3145i −0.478469 1.28553i
\(521\) −30.9193 −1.35460 −0.677299 0.735708i \(-0.736850\pi\)
−0.677299 + 0.735708i \(0.736850\pi\)
\(522\) 10.4596 2.43806i 0.457806 0.106711i
\(523\) −21.8385 −0.954932 −0.477466 0.878650i \(-0.658445\pi\)
−0.477466 + 0.878650i \(0.658445\pi\)
\(524\) −3.44018 6.97849i −0.150285 0.304857i
\(525\) 12.4596 16.0078i 0.543783 0.698636i
\(526\) −20.1949 + 4.70729i −0.880541 + 0.205248i
\(527\) 14.8550i 0.647092i
\(528\) 3.12811 + 2.40169i 0.136134 + 0.104520i
\(529\) 10.4876 0.455981
\(530\) −0.0737791 + 0.722984i −0.00320476 + 0.0314044i
\(531\) 9.10003i 0.394908i
\(532\) −18.9582 + 9.34579i −0.821940 + 0.405191i
\(533\) −2.81060 −0.121740
\(534\) −3.96511 17.0109i −0.171587 0.736133i
\(535\) −8.45963 2.90425i −0.365742 0.125562i
\(536\) 15.1755 + 18.4994i 0.655481 + 0.799052i
\(537\) 16.1746i 0.697986i
\(538\) −15.8913 + 3.70415i −0.685124 + 0.159697i
\(539\) 9.32662i 0.401726i
\(540\) −4.43594 + 0.567801i −0.190893 + 0.0244343i
\(541\) 24.3423i 1.04656i −0.852162 0.523278i \(-0.824709\pi\)
0.852162 0.523278i \(-0.175291\pi\)
\(542\) −1.80908 7.76120i −0.0777066 0.333372i
\(543\) 8.11409i 0.348209i
\(544\) 10.5683 23.3028i 0.453112 0.999098i
\(545\) 3.02792 8.81988i 0.129702 0.377802i
\(546\) 27.6351 6.44154i 1.18267 0.275673i
\(547\) 33.3789 1.42718 0.713589 0.700564i \(-0.247068\pi\)
0.713589 + 0.700564i \(0.247068\pi\)
\(548\) 15.4876 + 31.4169i 0.661596 + 1.34206i
\(549\) 11.0183i 0.470251i
\(550\) 6.33000 + 2.92145i 0.269912 + 0.124571i
\(551\) −19.7827 −0.842770
\(552\) 7.73530 6.34545i 0.329236 0.270080i
\(553\) 13.3239i 0.566592i
\(554\) 5.58774 + 23.9722i 0.237400 + 1.01848i
\(555\) 2.00000 + 0.686614i 0.0848953 + 0.0291451i
\(556\) 14.9108 + 30.2469i 0.632358 + 1.28275i
\(557\) 30.5808 1.29575 0.647875 0.761747i \(-0.275658\pi\)
0.647875 + 0.761747i \(0.275658\pi\)
\(558\) 1.05433 + 4.52323i 0.0446334 + 0.191484i
\(559\) 41.8385 1.76958
\(560\) −20.0474 30.2469i −0.847156 1.27816i
\(561\) −4.45963 −0.188286
\(562\) −6.99304 30.0011i −0.294984 1.26552i
\(563\) −7.02792 −0.296192 −0.148096 0.988973i \(-0.547314\pi\)
−0.148096 + 0.988973i \(0.547314\pi\)
\(564\) −2.30359 4.67289i −0.0969988 0.196764i
\(565\) −0.933181 + 2.71821i −0.0392592 + 0.114356i
\(566\) 6.93318 + 29.7443i 0.291423 + 1.25025i
\(567\) 4.05705i 0.170380i
\(568\) 2.56829 + 3.13083i 0.107763 + 0.131367i
\(569\) −24.3510 −1.02085 −0.510423 0.859924i \(-0.670511\pi\)
−0.510423 + 0.859924i \(0.670511\pi\)
\(570\) 8.19493 + 0.836276i 0.343248 + 0.0350278i
\(571\) 20.0992i 0.841125i −0.907263 0.420563i \(-0.861833\pi\)
0.907263 0.420563i \(-0.138167\pi\)
\(572\) 4.31207 + 8.74714i 0.180297 + 0.365736i
\(573\) −24.9193 −1.04102
\(574\) −3.17548 + 0.740182i −0.132542 + 0.0308946i
\(575\) 10.8634 13.9570i 0.453036 0.582047i
\(576\) −1.56406 + 7.84562i −0.0651690 + 0.326901i
\(577\) 4.76899i 0.198536i −0.995061 0.0992678i \(-0.968350\pi\)
0.995061 0.0992678i \(-0.0316501\pi\)
\(578\) 1.11067 + 4.76492i 0.0461977 + 0.198195i
\(579\) 1.03951i 0.0432004i
\(580\) −4.31207 33.6881i −0.179049 1.39882i
\(581\) 40.1296i 1.66486i
\(582\) −4.45963 + 1.03951i −0.184858 + 0.0430890i
\(583\) 0.226584i 0.00938413i
\(584\) 26.1336 21.4380i 1.08142 0.887112i
\(585\) −10.4596 3.59086i −0.432452 0.148464i
\(586\) −10.2772 44.0906i −0.424547 1.82136i
\(587\) −8.21733 −0.339165 −0.169583 0.985516i \(-0.554242\pi\)
−0.169583 + 0.985516i \(0.554242\pi\)
\(588\) 16.9694 8.36537i 0.699804 0.344982i
\(589\) 8.55495i 0.352501i
\(590\) −28.6282 2.92145i −1.17860 0.120274i
\(591\) −9.66152 −0.397422
\(592\) 2.30359 3.00034i 0.0946771 0.123313i
\(593\) 7.76120i 0.318714i 0.987221 + 0.159357i \(0.0509421\pi\)
−0.987221 + 0.159357i \(0.949058\pi\)
\(594\) 1.35793 0.316523i 0.0557164 0.0129871i
\(595\) 38.8106 + 13.3239i 1.59108 + 0.546228i
\(596\) −9.28415 18.8331i −0.380293 0.771434i
\(597\) −23.0668 −0.944062
\(598\) 24.0947 5.61631i 0.985307 0.229668i
\(599\) 5.64903 0.230813 0.115407 0.993318i \(-0.463183\pi\)
0.115407 + 0.993318i \(0.463183\pi\)
\(600\) 0.362165 + 14.1375i 0.0147853 + 0.577161i
\(601\) −37.7299 −1.53903 −0.769516 0.638627i \(-0.779503\pi\)
−0.769516 + 0.638627i \(0.779503\pi\)
\(602\) 47.2702 11.0183i 1.92659 0.449074i
\(603\) 8.45963 0.344503
\(604\) −8.45963 + 4.17034i −0.344217 + 0.169689i
\(605\) 21.2081 + 7.28090i 0.862233 + 0.296010i
\(606\) −6.00000 + 1.39856i −0.243733 + 0.0568124i
\(607\) 0.113292i 0.00459837i −0.999997 0.00229919i \(-0.999268\pi\)
0.999997 0.00229919i \(-0.000731854\pi\)
\(608\) 6.08627 13.4200i 0.246831 0.544254i
\(609\) 30.8106 1.24851
\(610\) −34.6630 3.53729i −1.40347 0.143221i
\(611\) 12.8831i 0.521194i
\(612\) −4.00000 8.11409i −0.161690 0.327993i
\(613\) 0.703366 0.0284087 0.0142044 0.999899i \(-0.495478\pi\)
0.0142044 + 0.999899i \(0.495478\pi\)
\(614\) −0.364887 1.56542i −0.0147256 0.0631750i
\(615\) 1.20189 + 0.412617i 0.0484649 + 0.0166383i
\(616\) 7.17548 + 8.74714i 0.289108 + 0.352432i
\(617\) 24.4809i 0.985564i 0.870153 + 0.492782i \(0.164020\pi\)
−0.870153 + 0.492782i \(0.835980\pi\)
\(618\) 20.7632 4.83975i 0.835219 0.194683i
\(619\) 39.4966i 1.58750i 0.608243 + 0.793751i \(0.291874\pi\)
−0.608243 + 0.793751i \(0.708126\pi\)
\(620\) 14.5683 1.86474i 0.585077 0.0748898i
\(621\) 3.53729i 0.141947i
\(622\) −1.64903 7.07459i −0.0661202 0.283665i
\(623\) 50.1084i 2.00755i
\(624\) −12.0474 + 15.6912i −0.482281 + 0.628152i
\(625\) 6.13659 + 24.2351i 0.245464 + 0.969406i
\(626\) −31.7827 + 7.40831i −1.27029 + 0.296095i
\(627\) −2.56829 −0.102568
\(628\) −16.0474 + 7.91086i −0.640360 + 0.315678i
\(629\) 4.27748i 0.170554i
\(630\) −12.7632 1.30246i −0.508499 0.0518913i
\(631\) 17.3400 0.690294 0.345147 0.938549i \(-0.387829\pi\)
0.345147 + 0.938549i \(0.387829\pi\)
\(632\) 5.89134 + 7.18172i 0.234345 + 0.285674i
\(633\) 6.44154i 0.256028i
\(634\) 0.533409 + 2.28840i 0.0211844 + 0.0908840i
\(635\) 0.837003 2.43806i 0.0332155 0.0967516i
\(636\) 0.412259 0.203231i 0.0163471 0.00805863i
\(637\) 46.7842 1.85366
\(638\) 2.40378 + 10.3126i 0.0951666 + 0.408278i
\(639\) 1.43171 0.0566374
\(640\) 24.1797 + 7.43916i 0.955787 + 0.294058i
\(641\) 38.7019 1.52863 0.764317 0.644840i \(-0.223076\pi\)
0.764317 + 0.644840i \(0.223076\pi\)
\(642\) 1.28415 + 5.50917i 0.0506812 + 0.217430i
\(643\) 1.13659 0.0448227 0.0224113 0.999749i \(-0.492866\pi\)
0.0224113 + 0.999749i \(0.492866\pi\)
\(644\) 25.7438 12.6909i 1.01445 0.500091i
\(645\) −17.8913 6.14222i −0.704471 0.241850i
\(646\) 3.78267 + 16.2282i 0.148827 + 0.638490i
\(647\) 6.54868i 0.257455i 0.991680 + 0.128728i \(0.0410893\pi\)
−0.991680 + 0.128728i \(0.958911\pi\)
\(648\) 1.79387 + 2.18678i 0.0704699 + 0.0859050i
\(649\) 8.97208 0.352185
\(650\) −14.6546 + 31.7526i −0.574799 + 1.24544i
\(651\) 13.3239i 0.522206i
\(652\) −28.3121 + 13.9570i −1.10879 + 0.546598i
\(653\) −8.74226 −0.342111 −0.171056 0.985261i \(-0.554718\pi\)
−0.171056 + 0.985261i \(0.554718\pi\)
\(654\) −5.74378 + 1.33883i −0.224599 + 0.0523525i
\(655\) −2.82452 + 8.22739i −0.110363 + 0.321471i
\(656\) 1.38433 1.80304i 0.0540492 0.0703969i
\(657\) 11.9507i 0.466242i
\(658\) −3.39281 14.5556i −0.132266 0.567438i
\(659\) 35.5336i 1.38419i −0.721804 0.692097i \(-0.756687\pi\)
0.721804 0.692097i \(-0.243313\pi\)
\(660\) −0.559817 4.37357i −0.0217908 0.170241i
\(661\) 23.3028i 0.906373i 0.891416 + 0.453186i \(0.149713\pi\)
−0.891416 + 0.453186i \(0.850287\pi\)
\(662\) −35.6825 + 8.31732i −1.38684 + 0.323262i
\(663\) 22.3704i 0.868795i
\(664\) −17.7438 21.6302i −0.688592 0.839415i
\(665\) 22.3510 + 7.67324i 0.866733 + 0.297555i
\(666\) −0.303594 1.30246i −0.0117640 0.0504694i
\(667\) 26.8634 1.04016
\(668\) −4.87189 9.88274i −0.188499 0.382375i
\(669\) 17.9796i 0.695133i
\(670\) 2.71585 26.6135i 0.104923 1.02817i
\(671\) 10.8634 0.419377
\(672\) −9.47908 + 20.9011i −0.365663 + 0.806277i
\(673\) 14.3634i 0.553670i 0.960917 + 0.276835i \(0.0892856\pi\)
−0.960917 + 0.276835i \(0.910714\pi\)
\(674\) 11.0279 2.57053i 0.424780 0.0990130i
\(675\) 3.94567 + 3.07111i 0.151869 + 0.118207i
\(676\) −20.5571 + 10.1340i −0.790658 + 0.389770i
\(677\) −24.3076 −0.934217 −0.467109 0.884200i \(-0.654704\pi\)
−0.467109 + 0.884200i \(0.654704\pi\)
\(678\) 1.77018 0.412617i 0.0679835 0.0158465i
\(679\) −13.1366 −0.504136
\(680\) −26.8106 + 9.97884i −1.02814 + 0.382671i
\(681\) −7.02792 −0.269311
\(682\) −4.45963 + 1.03951i −0.170768 + 0.0398048i
\(683\) −38.5933 −1.47673 −0.738365 0.674401i \(-0.764402\pi\)
−0.738365 + 0.674401i \(0.764402\pi\)
\(684\) −2.30359 4.67289i −0.0880801 0.178673i
\(685\) 12.7159 37.0393i 0.485848 1.41520i
\(686\) 13.7438 3.20357i 0.524740 0.122313i
\(687\) 4.17034i 0.159108i
\(688\) −20.6072 + 26.8401i −0.785642 + 1.02327i
\(689\) 1.13659 0.0433006
\(690\) −11.1281 1.13560i −0.423640 0.0432316i
\(691\) 13.4090i 0.510102i −0.966928 0.255051i \(-0.917908\pi\)
0.966928 0.255051i \(-0.0820923\pi\)
\(692\) 18.5459 9.14256i 0.705009 0.347548i
\(693\) 4.00000 0.151947
\(694\) −7.39281 31.7162i −0.280627 1.20393i
\(695\) 12.2423 35.6599i 0.464377 1.35266i
\(696\) −16.6072 + 13.6233i −0.629494 + 0.516389i
\(697\) 2.57053i 0.0973657i
\(698\) 29.5264 6.88240i 1.11759 0.260503i
\(699\) 23.9894i 0.907362i
\(700\) −8.19493 + 39.7342i −0.309739 + 1.50181i
\(701\) 15.6013i 0.589253i 0.955613 + 0.294626i \(0.0951952\pi\)
−0.955613 + 0.294626i \(0.904805\pi\)
\(702\) 1.58774 + 6.81163i 0.0599254 + 0.257089i
\(703\) 2.46339i 0.0929086i
\(704\) −7.73530 1.54206i −0.291535 0.0581187i
\(705\) −1.89134 + 5.50917i −0.0712318 + 0.207487i
\(706\) 6.22982 1.45212i 0.234462 0.0546514i
\(707\) −17.6740 −0.664699
\(708\) 8.04737 + 16.3243i 0.302439 + 0.613504i
\(709\) 15.7873i 0.592906i 0.955047 + 0.296453i \(0.0958038\pi\)
−0.955047 + 0.296453i \(0.904196\pi\)
\(710\) 0.459630 4.50406i 0.0172496 0.169034i
\(711\) 3.28415 0.123165
\(712\) 22.1560 + 27.0089i 0.830333 + 1.01220i
\(713\) 11.6170i 0.435060i
\(714\) −5.89134 25.2747i −0.220478 0.945880i
\(715\) 3.54037 10.3126i 0.132402 0.385668i
\(716\) −14.3036 29.0152i −0.534550 1.08435i
\(717\) 8.91926 0.333096
\(718\) 3.32304 + 14.2563i 0.124015 + 0.532041i
\(719\) −22.5683 −0.841655 −0.420828 0.907141i \(-0.638260\pi\)
−0.420828 + 0.907141i \(0.638260\pi\)
\(720\) 7.45539 4.94137i 0.277846 0.184154i
\(721\) 61.1616 2.27778
\(722\) −3.92126 16.8228i −0.145934 0.626079i
\(723\) −16.3510 −0.608099
\(724\) 7.17548 + 14.5556i 0.266675 + 0.540956i
\(725\) −23.3230 + 29.9647i −0.866196 + 1.11286i
\(726\) −3.21933 13.8114i −0.119481 0.512589i
\(727\) 2.79096i 0.103511i 0.998660 + 0.0517554i \(0.0164816\pi\)
−0.998660 + 0.0517554i \(0.983518\pi\)
\(728\) −43.8774 + 35.9937i −1.62621 + 1.33401i
\(729\) 1.00000 0.0370370
\(730\) −37.5962 3.83662i −1.39150 0.142000i
\(731\) 38.2649i 1.41528i
\(732\) 9.74378 + 19.7655i 0.360140 + 0.730553i
\(733\) −16.4860 −0.608926 −0.304463 0.952524i \(-0.598477\pi\)
−0.304463 + 0.952524i \(0.598477\pi\)
\(734\) −0.668481 + 0.155818i −0.0246741 + 0.00575135i
\(735\) −20.0062 6.86828i −0.737941 0.253340i
\(736\) −8.26470 + 18.2234i −0.304641 + 0.671724i
\(737\) 8.34068i 0.307233i
\(738\) −0.182443 0.782708i −0.00671584 0.0288119i
\(739\) 14.8894i 0.547714i 0.961770 + 0.273857i \(0.0882995\pi\)
−0.961770 + 0.273857i \(0.911701\pi\)
\(740\) −4.19493 + 0.536951i −0.154209 + 0.0197387i
\(741\) 12.8831i 0.473272i
\(742\) 1.28415 0.299325i 0.0471425 0.0109886i
\(743\) 41.4301i 1.51992i −0.649968 0.759961i \(-0.725218\pi\)
0.649968 0.759961i \(-0.274782\pi\)
\(744\) −5.89134 7.18172i −0.215987 0.263295i
\(745\) −7.62263 + 22.2035i −0.279271 + 0.813475i
\(746\) −9.65751 41.4321i −0.353587 1.51694i
\(747\) −9.89134 −0.361905
\(748\) 8.00000 3.94376i 0.292509 0.144198i
\(749\) 16.2282i 0.592965i
\(750\) 10.9282 11.4269i 0.399042 0.417251i
\(751\) 30.5544 1.11494 0.557472 0.830195i \(-0.311771\pi\)
0.557472 + 0.830195i \(0.311771\pi\)
\(752\) 8.26470 + 6.34545i 0.301383 + 0.231395i
\(753\) 4.22391i 0.153928i
\(754\) −51.7299 + 12.0578i −1.88389 + 0.439121i
\(755\) 9.97359 + 3.42400i 0.362976 + 0.124612i
\(756\) 3.58774 + 7.27782i 0.130485 + 0.264692i
\(757\) 0.433223 0.0157457 0.00787287 0.999969i \(-0.497494\pi\)
0.00787287 + 0.999969i \(0.497494\pi\)
\(758\) 46.3983 10.8151i 1.68526 0.392823i
\(759\) 3.48755 0.126590
\(760\) −15.4402 + 5.74680i −0.560074 + 0.208458i
\(761\) −14.9193 −0.540823 −0.270411 0.962745i \(-0.587160\pi\)
−0.270411 + 0.962745i \(0.587160\pi\)
\(762\) −1.58774 + 0.370091i −0.0575178 + 0.0134070i
\(763\) −16.9193 −0.612518
\(764\) 44.7019 22.0367i 1.61726 0.797259i
\(765\) −3.28415 + 9.56622i −0.118739 + 0.345867i
\(766\) 7.12811 1.66151i 0.257549 0.0600328i
\(767\) 45.0057i 1.62506i
\(768\) −4.13235 15.4572i −0.149113 0.557762i
\(769\) 31.3789 1.13155 0.565776 0.824559i \(-0.308577\pi\)
0.565776 + 0.824559i \(0.308577\pi\)
\(770\) 1.28415 12.5838i 0.0462775 0.453487i
\(771\) 24.6952i 0.889375i
\(772\) 0.919260 + 1.86474i 0.0330849 + 0.0671135i
\(773\) 13.4192 0.482656 0.241328 0.970444i \(-0.422417\pi\)
0.241328 + 0.970444i \(0.422417\pi\)
\(774\) 2.71585 + 11.6514i 0.0976193 + 0.418800i
\(775\) −12.9582 10.0860i −0.465471 0.362299i
\(776\) 7.08074 5.80850i 0.254184 0.208513i
\(777\) 3.83662i 0.137638i
\(778\) −22.9193 + 5.34231i −0.821695 + 0.191531i
\(779\) 1.48036i 0.0530395i
\(780\) 21.9387 2.80815i 0.785532 0.100548i
\(781\) 1.41157i 0.0505101i
\(782\) −5.13659 22.0367i −0.183684 0.788030i
\(783\) 7.59434i 0.271400i
\(784\)